Mathematics

On the number of faces of marked order polytopes

E. V. Melikhova

National Research University Higher School of Economics, Moscow

Abstract: We present a new method for computing the f -vector of a marked order polytope. Namely, given an arbitrary (polytopal) subdivision of an arbitrary convex polytope, we construct a cochain complex (over the two-element field Z2) such that the dimensions of its cohomology groups equal the components of the f -vector of the original polytope. In the case of a marked order polytope and its well-known cubosimplicial subdivision, this cochain complex can be described purely combinatorially, which yields the said computation of the f -vector. Of independent interest may be our combinatorial description of the said cubosimplicial subdivision (which was originally constructed geometrically).

Keywords: marked order polytope, f -vector, polyhedral complex

UDC: 514.172.45

Received: 16.04.2025
Accepted: 29.08.2025